In this note, we show how certain properties of Goldbeter's 1995 model for circadian oscillations can be proved mathematically, using techniques from the recently developed theory of monotone systems with inputs and outputs. The theory establishes global asymptotic stability, and in particular no oscillations, if the rate of transcription is somewhat smaller than that assumed by Goldbeter. This stability persists even under arbitrary delays in the feedback loop.
An analysis of a circadian model using the small-gain approach to monotone systems / Angeli, David; Sontag, Eduardo D.. - CD-ROM. - (2004), pp. 575-578. (Intervento presentato al convegno IEEE Conference on Decision and Control) [10.1109/CDC.2004.1428692].
An analysis of a circadian model using the small-gain approach to monotone systems
Angeli, David;
2004
Abstract
In this note, we show how certain properties of Goldbeter's 1995 model for circadian oscillations can be proved mathematically, using techniques from the recently developed theory of monotone systems with inputs and outputs. The theory establishes global asymptotic stability, and in particular no oscillations, if the rate of transcription is somewhat smaller than that assumed by Goldbeter. This stability persists even under arbitrary delays in the feedback loop.
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